Guia docente 2023_24
Escuela de Ingeniería Industrial
Máster Universitario en Ingeniería Biomédica
 Subjects
  Modelado e simulación sistemas biomédicos
   Contents
Topic Sub-topic
1. Introduction to mathematical modelling in biomedicine 1.1. Motivation and history of biomedical modelling
1.2. Dynamic modelling: components and paradigms
1.3. Types of dynamic models
1.3.1. Graphs
1.3.2. Differential equations
1.4. Combinations of models
1.5. Examples
2. Dynamical biomedical systems. Approaches to their modelling 2.1. Types of biosistems of interest
2.2. Biochemical reaction kinetics
2.3. Cellular level
2.3.1. Metabolism
2.3.2. Cellular signalling
2.3.3. Gene expression
2.4. Organ level
2.4.1. Electrophysiology
2.4.2. Glucose regulation
2.4.3. Pharmacokinetics and pharmacodynamics
2.5. Population level
2.5.1. Epidemiology
2.5.2. Microbial communities
3. Numerical simulation methods 3.1. Integration of linear ordinary differential equations
3.1.1. Laplace transform
3.1.2. Transfer function
3.2. Integration of nonlinear ordinary differential equations
3.2.1. Fixed step methods
3.2.2. Variable step methods
3.3. Integration of stochastic equations
3.3.1. Gillespie algorithm
3.4. Simulation software
3.4.1. General purpose programming environments
3.4.2. Specialized simulation tools
3.5. Standards, formats, and repositories
4. Model building and system identification 4.0. STEP 0: obtain the equations of the model
4.1. STEP 1: analyse observability and structural identifiability
4.2. STEP 2: define the objective function
4.3. STEP 3: parameter optimization
4.3.1. Local methods
4.3.2. Global methods
4.3.3. Definition of the optimization problem
4.4. STEP 4: analysis of the goodness of fit
4.5. STEP 5: Parameter uncertainty quantification
4.6. STEP 6: Prediction uncertainty quantification
4.7. Experimental design
4.8. Model selection
4.9. Computational resources
5. Dynamic behaviour 5.1. Equilibrium and stability
5.1.1. Mathematical characterization of stability
5.2. Bifurcations
5.3. Oscillations
5.4. Robustness
5.4.1. Redundancy
5.4.2. Parametric insensitivity
5.4.3. Feedback
5.4.4. Feedforward loops
5.5. Model reduction
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